That's a bit of a misnomer, BA. They can't see exact keystrokes, especially not if the website is over HTTPS
The likelihood is that the owner of the public wifi hotspot is keeping logs of what gets accessed, but the majority of the time only for compliance with relevant laws. If, for example, someone were to view banned material over such a connection, the owner needs to be able to identify them. If they do not, then they themselves are liable, and could go to jail.
It is also worth thinking about the number of users who use the service. They don't have time to look at all those logs.
The other people who can snoop are, as BA says, other people who have the right tools on their laptop or other device. Because the stuff you're sending is not encrypted (unless you are using HTTPS), it is possible to sniff the traffic, and see what people are doing. They would need to be connected to the same wifi, however, and there is the requirement for physical proximity to sniff such traffic.
Again, there is the question of motive. For stuff like forum traffic, people probably won't care. They'll be on the look out for more 'juicy' data such as emails, banks etc.
Then there is the third point BA mentions, which is that there is no 100% guarantee that the free wifi belongs to who it says does.
Big companies will combat this with wIPS, which basically uses their access points to muscle out anyone pretending to be them. Smaller companies won't be able to afford the expensive systems that it takes to do that, and as such are more likely to suffer from this kind of attack. I know it has been well documented that there have been occasions where a security expert has set up a 'free wifi' and people just connect without thinking twice.
So in summary, check with the owner of the establishment that they provide free wifi, make sure that the network name to which you are connecting matches what they think it should be. If you're transmitting personal info, use HTTPS (there will be a padlock icon on your browser) and steer clear of illegal sites!